**Numerical Investigation on the Swimming of Gyrotactic Microorganisms in Nanofluids through Porous Medium over a Stretched Surface**

### **Anwar Shahid 1, Hulin Huang 1, Muhammad Mubashir Bhatti 2, Lijun Zhang 2 and Rahmat Ellahi 3,4,5,\***


Received: 16 February 2020; Accepted: 5 March 2020; Published: 9 March 2020

**Abstract:** In this article, the e ffects of swimming gyrotactic microorganisms for magnetohydrodynamics nanofluid using Darcy law are investigated. The numerical results of nonlinear coupled mathematical model are obtained by means of Successive Local Linearization Method. This technique is based on a simple notion of the decoupling systems of equations utilizing the linearization of the unknown functions sequentially according to the order of classifying the system of governing equations. The linearized equations, that developed a sequence of linear di fferential equations along with variable coe fficients, were solved by employing the Chebyshev spectral collocation method. The convergence speed of the SLLM technique can be willingly upgraded by successive applying over relaxation method. The comparison of current study with available published literature has been made for the validation of obtained results. It is found that the reported numerical method is in perfect accord with the said similar methods. The results are displayed through tables and graphs.

**Keywords:** successive local linearization method; swimming gyrotactic microorganisms; Darcy law; nanofluid
